Darlington Transistor Working Explained with Calculations

In this post you will learn about this amazing BJT device called the Darlington Transistor. It was named after this genius engineer, Sidney Darlington, who came up with the idea.

Basically it is like a special combo of two regular NPN or PNP bipolar junction transistors (BJTs) that are hooked up in a clever way.

What happens is that the Emitter of one transistor connects to the Base of the other which makes this new setup super sensitive and gives it a much bigger current gain.

This is really handy when you need to amplify current or do some switching action.

Now if you are wondering how these Darlington pairs work, they can either be made from two separate BJTs connected together or you can find them as a single device that is all packaged up nicely.

This single package has the usual connections like Base, Emitter, and Collector, and you can get them in all sorts of styles and ratings for voltage and current, both in NPN and PNP flavors.

Remember when we talked about transistors acting as switches? Just like in our tutorial on Transistor as a Switch, these bipolar junction transistors can also do that ON-OFF switching and can be also used as amplifiers. So these devices are hugely versatile!

In short, a Darlington Transistor is like having two transistors working together to give you a huge boost in current gain from just a tiny input base current. This means that you can control bigger loads using negligible input base voltage and current, from things like microcontrollers or sensors. Super efficient, right?

Plus, there are even special types like the complementary Sziklai Darlington transistors that mix NPN and PNP transistors together for even better efficiency.

How a BJT Works Like a Switch

Now let us revise how the NPN transistor works as a switch, especially when we are talking about its base terminal being grounded.

So, suppose we ground the base terminal to 0 volts which means that the base current or Ib is basically zero.

Because the base is grounded, there is no way for current to flow from the collector to the emitter. So now this NPN transistor is in its non-conducting state which we call “OFF,” or in technical terms it is in the cut-off region.

Now if you take a voltage source and apply a positive voltage greater than 0.7 volts to the base terminal, basically forward biasing it with respect to the emitter, the BJT gets activated!

This forward biasing allows a much larger current to flow through from the collector to its emitter. At this point, we say that the transistor is switched “ON” and is now conducting.

So, if we keep toggling between these two states, cut-off (OFF) and conduction (ON), we can actually use this NPN transistor as an electronic switch. It is like having a light switch where I can turn it on and off by just switching the voltage at the base.

But for the above NPN BJT to really conduct fully we need to switch the base terminal between zero volts and some positive voltage that needs to be at least 0.7 volts.

When we increase that voltage, it pumps more base current or Ib into the transistor. This surge in base current leads to a big increase in the collector current or Ic while at the same time, the voltage drop across the collector and emitter terminals, which we call Vce gets smaller.

What is interesting here is that just a little bit of current flowing into the base can trigger a much larger current to flow between the collector and emitter.

Now let us discuss the current gain of the transistor, which is represented by the ratio of collector current to base current (that’s our β).

For a typical bipolar transistor, we can expect β to be somewhere between 50 and 200. But even transistors that have the same part number can have different values of β.

Sometimes while working with amplifier circuits, whenever I find that a single transistor just does not have enough current gain to drive a load directly, I can simply set up a Darlington pair. This setup combines two transistors to give me a much higher gain, making it easier to control bigger loads without any hassles.

A Darlington BJT configuration, which is often referred to as a “Darlington pair” or a “super-alpha circuit,” consists of two transistors either NPN or PNP types, that are interconnected in such a way that the emitter current of the first transistor, let us say TR1, serves as the base current for the second transistor TR2. In this setup we configure TR1 as an emitter follower while TR2 operates as a common emitter amplifier as illustrated in the diagram below.

It is also important to highlight that in this Darlington pair configuration, the collector current of the first transistor, TR1, often referred to as the slave or control transistor, flows in-phase with the collector current of the second transistor TR2 which acts as the master switching transistor.

Analyzing a Typical Darlington Transistor Configuration

In NPN Darlington pair arrangement we observe that the collectors of the two transistors are interconnected, while the emitter of the first transisto, which is TR1, is responsible for driving the base of the second transistor TR2.

This specific configuration allows for what is known as the β multiplication, a phenomenon that significantly enhances current gain. To illustrate this concept let us consider a base current denoted as ib. In this scenario the collector current can be expressed as: IC = β * i_b, where β represents the current gain which is invariably greater than one or unity.

This relationship can be mathematically defined as follows:

I_C = I_C1 + I_C2
I_C = β₁ * I_B + β₂ * I_B

In this context, it is important to note that the base current I_B2 of T_R2 is equivalent to the emitter current I_E1 of T_R1.

This equivalence arises because the emitter of TR1 is directly connected to the base of TR2.

So, we can express this relationship as:

I_B2 = I_E1 = I_C1 + I_B

= β₁ * I_B + I_B
= (β₁ + 1) * I_B

Next, further substituting this in the first equation gives us:

I_C = β₁ * I_B + β₂ * (β₁ + 1) * I_B

I_C = β₁ * I_B + β₂ * β₁ * I_B + β₂ * I_B

I_C = (β₁ + (β₂ * β₁) + β₂) * I_B

The terms β1 and β2 indicate the gains of those individual transistors. What this tells us is that if we want to calculate the total current β, we simply take the gain of the first transistor and multiply it by the gain of the second one.

It is so good, because the current gains of these two transistors actually combine together in this multiplication process.

To put it in simpler terms when we configure a couple of bipolar transistors to create a Darlington transistor pair, we can think of them as functioning like one single transistor.

So, this combined setup gives us a super high value of β which means we also end up getting a really high input resistance.

Solving a Darlington Pair Transistor Problem #1

we’ve got this setup where we’re connecting two NPN transistors together to create a Darlington Pair. The purpose of this configuration is to control a 12V, 100W halogen lamp.

The first transistor has a forward current gain of 30, while the second BJT features a forward current gain or Beta of 100.

For our calculations we are going to ignore any voltage drops that might occur across these two transistors because we want to keep things simple.

We want to calculate the maximum base current that we will need to switch this halogen lamp fully ON. 

It is evident that the current consumed by the lamp has to be equal to the Collector current of the second BJT, therefore we can use the following formula:

I_C = I_LAMP

I_LAMP = P/V = 100/12 = 8.33 Amps

By referring to our earlier derived β formulas, we can calculate the base current of the first BJT as:

I_C = (β₁ + (β₂ * β₁) + β₂) * I_B

I_B = I_C/(β₁ + (β₂ * β₁) + β₂)

= 8.33/((30 + (100 * 30) + 100) = 0.00266 Amps or 2.66 mA

So, we can see that we only need a very tiny base current of just 2.66 mA to get that 100 watt lamp to turn “ON” and “OFF.” This small base current can easily be provided by something like a digital logic gate or even the output port of a micro-controller. It is pretty impressive how we can control such a powerful lamp with just a negligible amount of of input current.

Now let us talk about what happens when we use two identical bipolar transistors to create a single Darlington device. In this case we find that β₁ is equal to β₂ which means that both the transistors have the same gain.

Because β₁ is equal to β₂ the total current gain for this setup can be calculated as follows:

I_C = (β₁ + (β₂ * β₁) + β₂) * I_B

∴ I_C = (β² + 2β) * I_B

Typically we find that the value of β² is way higher than 2β. Because of this big difference we can actually ignore the 2β part to make our calculations a bit simpler.

So when we are looking at two identical transistors that are set up as a Darlington pair, we can simply use a final equation that reflects this configuration, as given below:

I_C = (β² * I_B)

So when we are looking at two identical transistors, we can see that β² essentially takes the place of β. This means that they work together like one big transistor that has a really impressive gain.

You can actually find Darlington transistor pairs that have current gains that go beyond one thousand and can handle maximum collector currents of several amperes.

A couple of great examples of this are the NPN BJT TIP122 and its PNP complementary, the TIP127. Now one of the best things about using this kind of setup is that the switching transistor becomes super sensitive.

This is because it only needs a tiny base current to control a much larger load current. For example, the typical gain for a Darlington configuration is over 1,000, but if we were just using a standard single transistor stage, we would get a gain of just around 50 to 200.

So if we have a Darlington pair with a gain of 1,000:1 we could control an output current of 1 ampere in the collector-emitter circuit using just a miniscule input base current of only 1 mA.

This makes Darlington transistors absolutely ideal for interfacing with relays, lamps, and motors when we are working with sources such as low-power microcontrollers, computers, or logic controllers.

Understanding Applications of Darlington Transistor

When we are talking about a Darlington transistor, one of the good things is that its base is really sensitive.

This means that it can easily respond to small input currents, whether those are coming from a switch or directly from something like a TTL or 5V CMOS logic gate.

Now when we look at the maximum collector current Ic(max), it is actually equivalent to the main switching transistor in the second part of the Darlington pair, often referred to as TR2.

This allows us to control all types of devices such as relays, DC motors, solenoids, and lamps without any hassle using a Darlington BJT pair.

But there is a bit of a downside to using a Darlington transistor pair. One major drawback is the relatively low voltage drop between the base and emitter when it is fully saturated.

If we compare it to a single BJT, which typically has a saturated voltage drop between 0.3V and 0.7V when it is in full-ON mode, a Darlington component actually shows a higher base-emitter voltage drop of around 1.2V instead of just 0.6V.

This happens because that base-emitter voltage drop includes the combined drops from the base-emitter diodes of both transistors in the pair.

Depending on how much current is flowing through the transistors, this combined drop can vary anywhere from 0.6V to 1.5V.

When we talk about the high base-emitter voltage drop in a Darlington transistor, what we are really saying is that this Darlington device tends to get a lot hotter compared to the regular single bipolar transistor when we are pushing the same load current.

Because of this extra heat, it becomes extremely important for us to have some solid heat sinking in place to keep things cool.

Now, the fact that Darlington transistors are not exactly the fast switching devices in the transistor world. They have this slower ON-OFF response time because it takes a bit longer for the slave transistor, which we call TR1, to flip the master transistor TR2, either all the way ON or all the way OFF.

But no need to worry! There’s a way to tackle those slow response times and the extra voltage drop and heat issues that come with your standard Darlington transistor setup. We can use complementary NPN and PNP transistors in a similar cascaded arrangement, which gives us a different kind of Darlington transistor known as a Sziklai Configuration.

What is Sziklai Transistor Pair

Now let us discuss the Sziklai Transistor Pair which is also known as the Sziklai Darlington Pair. This setup is actually named after the Hungarian inventor George Sziklai. This is a complementary or compound device that uses an NPN and a PNP transistor paired together in a special way like in the diagram below.

The beauty of this NPN-PNP pairing is that it works a lot like a regular Darlington transistor setup but with a nice advantage. It only needs a base-emitter voltage of about 0.6V to turn on. So, it is more efficient in that regard.

And just like a standard Darlington, the Sziklai configuration also effectively boosts the current gain. If we use transistors with matching gain values, the overall current gain will be β². For transistors with different individual gains, the total gain is the product of those two gains, making it a versatile alternative.

Understanding the Sziklai Darlington Transistor Configuration

In the diagram above we can observe that the base-emitter voltage drop in the Sziklai device is equivalent to the diode drop found in a single transistor within the signal path.

However there is an important limitation to note, the Sziklai configuration cannot achieve saturation below a full diode drop, which typically measures around 0.7 volts, as opposed to the more common 0.2 volts seen in other configurations.

Additionally, similar to the behavior of the Darlington pair, the Sziklai pair experiences slower response times compared to a single transistor.

This characteristic can impact performance in certain applications. The complementary transistors that make up the Sziklai pair are frequently utilized in push-pull and class AB audio amplifier output stages, allowing us to work with just one polarity of output transistor.

It is also worth mentioning that both Darlington and Sziklai transistor pairs are readily available in both NPN and PNP configurations, providing flexibility for various circuit designs.

Understanding Darlington Transistor available as Integrated Circuits or ICs.

In most electronics projects, we usually just need the controlling circuit to turn a DC output voltage or current “ON” or “OFF” directly. This works fine for output devices like LEDs or displays that only need a few milliamps to run at low DC voltages, so we can drive them straight from a standard logic gate.

But sometimes, as we have seen, we need more power to run something like a DC motor than what an ordinary logic gate or microcontroller can provide. If the digital logic device can’t supply enough current, we’ll need some extra circuitry to get the job done.

One popular option for this is the ULN2003 Darlington transistor chip. This family of Darlington arrays includes the ULN2002A, ULN2003A, and ULN2004A, all of these ICs are high voltage and high current Darlington arrays. Each of these chips has seven open collector Darlington pairs packed into a single IC.

Each channel in the array can handle 500mA and can even take peak currents up to 600mA, making it perfect for controlling small motors, lamps, or even the gates and bases of high-power semiconductors.

Plus, it comes with extra suppression diodes for driving inductive loads, and the inputs are arranged opposite the outputs to make our connections and board layout easier.

The ULN2003A Darlington Transistor Array

Now, referring to the ULN2003A Darlington Transistor Array. It is an affordable unipolar Darlington transistor array that is super efficient and uses low power which makes it great for driving a variety of loads like solenoids, relays, DC motors, and LED displays or filament lamps.

The ULN2003A has seven Darlington transistor pairs, with an input pin on the left side and an output pin on the right side, just like we see in the diagram.

The ULN2003A Darlington driver is a highly efficient integrated circuit notable for its “extremely high input impedance” and substantial current gain, enabling it to be directly driven by either TTL (Transistor-Transistor Logic) or +5V CMOS (Complementary Metal-Oxide-Semiconductor) logic gates.

For applications requiring +15V CMOS logic, the ULN2004A variant is recommended, while for switching voltages that can reach up to 100V, the SN75468 Darlington array is the more suitable choice.

When an input pin (ranging from pins 1 to 7) is activated to a “HIGH” state, the corresponding output will transition to a “LOW” state, effectively sinking current.

Conversely when the input is set to a “LOW” state, the associated output enters a high impedance state. This high impedance “OFF” state serves to block load current and minimizes leakage current through the device, thereby enhancing overall efficiency.

In terms of connections, pin 8 (GND) should be linked to the ground or 0 volts of the load, while pin 9 (Vcc) connects to the load’s power supply.

Any load must be connected between +Vcc and one of the output pins (pins 10 to 16). For inductive loads like motors, relays, and solenoids, it is crucial that pin 9 is connected directly to Vcc to ensure proper functionality.

The ULN2003A is capable of switching currents of up to “500mA (0.5A)” per channel. If higher switching current capabilities are necessary then users can parallel both the inputs and outputs of the Darlington pairs. For instance, if we connect input pins 1 and 2 together along with output pins 16 and 15, it will allow us to get increased current handling when driving a load.

Conclusion

The Darlington Transistor is a powerful semiconductor device that stands out because its current and voltage ratings are much higher than those of regular small signal junction transistors. This makes it very useful in many electronic applications.

When we look at standard high power NPN or PNP transistors, we find that their DC current gain values are relatively low, sometimes as low as 20 or even less. This is quite different from small signal switching transistors, which usually have higher gains.

Because of this lower gain, larger base currents are needed to switch a specific load, which can make these transistors less efficient.

The Darlington arrangement uses two transistors connected back to back. One of these transistors carries the main current, while the other smaller transistor acts as a “switch” to provide a preamplified base current needed for the main transistor.

This setup allows us to use a smaller base current to control a much larger load current. The DC current gains of the two transistors multiply together, making it possible to think of them as one single transistor with a very high current gain (β) and high input resistance.

In addition to the standard PNP and NPN Darlington pairs, we also have complementary Sziklai Darlington transistors.

These consist of matching NPN and PNP transistors connected together in the same pair, which helps improve efficiency.

We can also use Darlington arrays like the ULN2003A. These arrays allow us to safely control high power or inductive loads such as lamps, solenoids, and motors using microprocessors and microcontrollers.

This feature is especially useful in robotic and mechatronic applications where precise control is important.

Sources:

Darlington transistor

Trying to understand how a darlington transistor works